EE 3220: Digital Communication Lec-3: Baseband transmission and Matched filter Dr. Hassan Yousif Ahmed Department of Electrical Engineering College of Engineering at Wadi Aldwasser Slman bin Abdulaziz University Dr Hassan Yousif

Last time we talked about: Transforming the information source to a form compatible with a digital system Sampling Aliasing Quantization Uniform and non-uniform Baseband modulation Binary pulse modulation M-ary pulse modulation M-PAM (M-ary Pulse amplitude modulation)‏ Dr Hassan Yousif

Formatting and transmission of baseband signal Digital info. Bit stream (Data bits)‏ Pulse waveforms (baseband signals)‏ Information (data) rate: Symbol rate : For real time transmission: Textual info. Format source Pulse modulate Sample Quantize Encode Analog info. Sampling at rate (sampling time=Ts)‏ Encoding each q. value to bits (Data bit duration Tb=Ts/l)‏ Quantizing each sampled value to one of the L levels in quantizer. Mapping every data bits to a symbol out of M symbols and transmitting a baseband waveform with duration T Dr Hassan Yousif

Quantization example Quant. levels boundaries x(nTs): sampled values amplitude x(t)‏ x(nTs): sampled values xq(nTs): quantized values boundaries Quant. levels 111 3.1867 110 2.2762 101 1.3657 100 0.4552 011 -0.4552 010 -1.3657 001 -2.2762 000 -3.1867 Ts: sampling time t PCM codeword 110 110 111 110 100 010 011 100 100 011 PCM sequence Dr Hassan Yousif

Example of M-ary PAM Assuming real time transmission and equal energy per transmission data bit for binary-PAM and 4-ary PAM: 4-ary: T=2Tb and Binary: T=Tb Binary PAM (rectangular pulse)‏ 4-ary PAM (rectangular pulse)‏ 3B A. ‘1’ ‘11’ B T T ‘01’ T T ‘10’ ‘00’ T T ‘0’ -B -A. -3B Dr Hassan Yousif

Example of M-ary PAM … 2.2762 V 1.3657 V 1 1 0 1 0 1 Rb=1/Tb=3/Ts 0 Ts 2Ts 2.2762 V 1.3657 V 0 Tb 2Tb 3Tb 4Tb 5Tb 6Tb 1 1 0 1 0 1 Rb=1/Tb=3/Ts R=1/T=1/Tb=3/Ts 0 T 2T 3T 4T 5T 6T Rb=1/Tb=3/Ts R=1/T=1/2Tb=3/2Ts=1.5/Ts 0 T 2T 3T Dr Hassan Yousif

Today we are going to talk about: Receiver structure Demodulation (and sampling)‏ Detection First step for designing the receiver Matched filter receiver Correlator receiver Dr Hassan Yousif

Demodulation and detection Format Pulse modulate Bandpass modulate M-ary modulation channel transmitted symbol Major sources of errors: Thermal noise (AWGN)‏ disturbs the signal in an additive fashion (Additive) has flat spectral density for all frequencies of interest (White)‏ is modeled by Gaussian random process (Gaussian Noise) Inter-Symbol Interference (ISI)‏ Due to the filtering effect of transmitter, channel and receiver, symbols are “smeared”. estimated symbol Format Detect Demod. & sample Dr Hassan Yousif

Example: Impact of the channel Dr Hassan Yousif

Example: Channel impact … Dr Hassan Yousif

Receiver tasks Demodulation and sampling: Detection: Waveform recovery and preparing the received signal for detection: Improving the signal power to the noise power (SNR) using matched filter Reducing ISI using equalizer Sampling the recovered waveform Detection: Estimate the transmitted symbol based on the received sample Dr Hassan Yousif

Receiver structure Step 1 – waveform to sample transformation Step 2 – decision making Demodulate & Sample Detect Threshold comparison Frequency down-conversion Receiving filter Equalizing filter Compensation for channel induced ISI For bandpass signals Received waveform Baseband pulse (possibly distored)‏ Baseband pulse Sample (test statistic)‏ Dr Hassan Yousif

Baseband and bandpass Bandpass model of detection process is equivalent to baseband model because: The received bandpass waveform is first transformed to a baseband waveform. Equivalence theorem: Performing bandpass linear signal processing followed by heterodyning the signal to the baseband, yields the same results as heterodyning the bandpass signal to the baseband , followed by a baseband linear signal processing. Dr Hassan Yousif

Steps in designing the receiver Find optimum solution for receiver design with the following goals: Maximize SNR Minimize ISI Steps in design: Model the received signal Find separate solutions for each of the goals. First, we focus on designing a receiver which maximizes the SNR. Dr Hassan Yousif

Design the receiver filter to maximize the SNR Model the received signal Simplify the model: Received signal in AWGN AWGN Ideal channels AWGN Dr Hassan Yousif

Matched filter receiver Problem: Design the receiver filter such that the SNR is maximized at the sampling time when is transmitted. Solution: The optimum filter, is the Matched filter, given by which is the time-reversed and delayed version of the conjugate of the transmitted signal Dr Hassan Yousif T t T t

Example of matched filter T 2T t T/2 T t T/2 T T t T/2 T 3T/2 2T t Dr Hassan Yousif

Properties of the matched filter The Fourier transform of a matched filter output with the matched signal as input is, except for a time delay factor, proportional to the ESD of the input signal. The output signal of a matched filter is proportional to a shifted version of the autocorrelation function of the input signal to which the filter is matched. The output SNR of a matched filter depends only on the ratio of the signal energy to the PSD of the white noise at the filter input. Two matching conditions in the matched-filtering operation: spectral phase matching that gives the desired output peak at time T. spectral amplitude matching that gives optimum SNR to the peak value. Dr Hassan Yousif

Correlator receiver The matched filter output at the sampling time, can be realized as the correlator output. Dr Hassan Yousif

Implementation of matched filter receiver Bank of M matched filters Matched filter output: Observation vector Dr Hassan Yousif

Implementation of correlator receiver Bank of M correlators Correlators output: Observation vector Dr Hassan Yousif

Implementation example of matched filter receivers Bank of 2 matched filters T t T T T t Dr Hassan Yousif